An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.

Archimedes, the original physicist and mathematician, was apparently responsible for coming up with the fundamental ideas for calculus. Although it might be safe to say that neither Newton nor Leibnitz actually knew this, they have to forego the privelege to having stumbled onto the thought first.

Whatdya know ?! Its PI day again. I remember posting on this day, last year about the same event and now, here we are again ! And in case you didn’t know, today is also the birthday of ‘Dr. Einstein’ of the E=mc2 fame 😉Here’s a tribute to this magic number, π:

History:

Biblical References: I Kings 7:23 II Chronicles 4:2In Kings, it states, “And he made a molten sea, ten cubits from one brim to the other: it was round all about, and a line of thirty cubits did compass it about.”

In 240 B.C, Archimedes of Syracuse, Sicily (287 – 212 BC) did the first theoretical calculation of . He used methods similar to the ones used by Euclid by inscribing a regular polygon inside a circle. He started with a hexagon and then polygons of 12, 24, 48, and finally 96 sides. He also used one of Euclid’s theorems to develop a numerical method for calculating the perimeter of the polygons. Archimedes obtained the approximation 223/71 < π < 22/7.

150 A.D. Ptolemy found π to be approximately 377/120 (or 3.1416)

480 A.D. In China, pi was found to be approximately equal to 355/113 or 3.1415929 …

In September 2002, π was computed to 1,240,000,000,000 decimal places by Professor Yasumasa Kanada at the University of Tokyo. It took over 400 hours on a Hitachi Supercomputer.

Facts and interesting stuff:

All the digits of Pi can never be fully known.

William Jones, a self-taught English mathematician born in Wales, is the one who selected the Greek letter π for the ratio of a circle’s circumference to its diameter in 1706.

Thirty divided by ten gives a value of 3. However, it is interesting to note that the word circumference happens to be spelled with an extra letter. Since in Hebrew all letters are also numbers, if we take the ratio of the value for the word as it is written (111) to the normal spelled word (106) we get the number 1.047169811… If you multiply this number by 3 you get 3.141509434… An amazingly close approximation to π!

The 1983 Guinness Book of World Records lists Rajan Mahadevan from India as having recited 31,811 places of pi from memory !

PI poem by Lorreen Pelletier: The number of letters in each line corresponds to a digit in the number &#960, up to 35 decimal places.

e raised to the i*pi power equals -1 (e is the base of the natural logarithm and i is the imaginary number which is the sqare root of -1)

Alternate π addendum:

Book:The life of PI – Here PI is an Indian guy’s name who gets stranded in the sea for more than 250 days. Its a good read although it has nothing to do with the π we are dealing with here. Just thought that might be an interesting trivia !Movie:PI – The movie starts with the line “When I was a little kid, my mother told me not to stare into the sun, so when I was six I did…”. Now with a line like that, how could i not watch it ! I’d recommend this movie to anyone who’s a little perceptive and frankly, a bit obsessed on math or anything for that matter. I watched the movie and loved it but few of my friends hated me for recommending the movie. So, there you go. But seriously, if you get some time, and are a math fan, watch it !

Today on Slashdot, a message board challenge to assemble a catalog of favority math and logic riddles. Well not all of them are that great but they have some really interesting puzzles among the lot.

There is a king and there are his n prisoners. The king has a dungeon in his castle that is shaped like a circle, and has n cell doors around the perimeter, each leading to a separate, utterly sound proof room. When within the cells, the prisoners have absolutely no means of communicating with each other.

The king sits in his central room and the n prisoners are all locked in their sound proof cells. In the king’s central chamber is a table with a single chalice sitting atop it. Now, the king opens up a door to one of the prisoners’ rooms and lets him into the room, but always only one prisoner at a time! So he lets in just one of the prisoners, any one he chooses, and then asks him a question, “Since I first locked you and the other prisoners into your rooms, have all of you been in this room yet?” The prisoner only has two possible answers. “Yes,” or, “I’m not sure.” If any prisoner answers “yes” but is wrong, they all will be beheaded. If a prisoner answers “yes,” however, and is correct, all prisoners are granted full pardons and freed. After being asked that question and answering, the prisoner is then given an opportunity to turn the chalice upside down or right side up. If when he enters the room it is right side up, he can choose to leave it right side up or to turn it upside down, it’s his choice. The same thing goes for if it is upside down when he enters the room. He can either choose to turn it upright or to leave it upside down. After the prisoner manipulates the chalice (or not, by his choice), he is sent back to his own cell and securely locked in.

The king will call the prisoners in any order he pleases, and he can call and recall each prisoner as many times as he wants, as many times in a row as he wants. The only rule the king has to obey is that eventually he has to call every prisoner in an arbitrary number of times. So maybe he will call the first prisoner in a million times before ever calling in the second prisoner twice, we just don’t know. But eventually we may be certain that each prisoner will be called in ten times, or twenty times, or any number you choose.

Here’s one last monkey wrench to toss in the gears, though. The king is allowed to manipulate the cup himself, k times, out of the view of any of the prisoners. That means the king may turn an upright cup upside down or vice versa up to k times, as he chooses, without the prisoners knowing about it. This does not mean the king must manipulate the cup any number of times at all, only that he may.

Also, found this great resource of riddles over at UCB’s site from the slashdot post. Definitely worth checking out if you have an hour or two to spare on some good grey cell petrifying puzzles.

Update : While we are at solving puzzles, here is one more awesome question that i had worked on, a long time back. Dig this.

You have a port that you are reading numbers from. You know that there is one number that is generated in more than half of the cases. You keep reading numbers arbitrarily long until you are given a command to stop. When you stop you have to return the number that has occurred in more than half of the cases.

I am not drunk and babbling gibberish. This is news. One fundamental theory which aims to make the use of trigonometry easier and more accurate. Proposed by Dr Norman Wildberger, a professor at University of New South Wales, this theory replaces angles to which we are so much used to by now, with a concept called as ‘spread’.

Established by the ancient Greeks and Romans, trigonometry is used in surveying, navigation, engineering, construction and the sciences to calculate the relationships between the sides and vertices of triangles.

“Generations of students have struggled with classical trigonometry because the framework is wrong,” says Wildberger, whose book is titled Divine Proportions: Rational Trigonometry to Universal Geometry (Wild Egg books).

Dr Wildberger has replaced traditional ideas of angles and distance with new concepts called “spread” and “quadrance”.

These new concepts mean that trigonometric problems can be done with algebra,” says Wildberger, an associate professor of mathematics at UNSW.

On first look, the concepts are straightforward in a logical sense. But i do not see how it simplifies and eliminates the calculations that are presently being done with sines and cosines. Well that’s just me and i could be wrong ! Maybe this is a revolutionary theory that is going to change how we look at things in the future.

Disclaimer

All posts on this site are solely my opinions, thoughts and prejudiced rants on various topics that interest me. These are my own philosophies that drive and help my evolution and may not apply to my random readers from varied backgrounds.

Life's beauty lies solely in the process of going up alleys to see if they are blind. And that is your curiosity and everyone's research. So be curious, learn and explore...